A particle swarm optimization approach on economic and economic-statistical designs of MEWMA control charts

Control charts are the best tools to monitor main process parameters, and the Multivariate Exponentially Weighted Moving Average, MEWMA, type of this tool is used when there are several correlated quality characteristics to be monitored simultaneously where detecting small deviations of the characteristics is desired. In this paper, the models of both the economic and the economic-statistical design problems of MEWMA control charts are solved by a Particle Swarm Optimization (PSO) approach. The comparison study between the economic and the economic-statistical designs shows better statistical performances of the economic-statistical design with negligible increase in cost. Furthermore, in order to demonstrate the application of the proposed methodology and to evaluate its performances, a comparative study is performed between Hooke and Jeeves [Hooke, R. and Jeeves, T.A. “Direct search solution of numerical and statistical problems”, Journal of the Association for Computing Machinery, 8, pp. 212–229 (1961)] method and the proposed method. The results show that the proposed PSO leads to better performances. At the end, some sensitivity analysis on the main parameters of the control chart and the cost parameters are presented.